Rivers was 8 of 14 from the field and 4 of 9 from 3 for the Seahawks (12-3, 3-1 Northeast Conference), who finished shooting 54 percent overall (27 of 50).
Jonathan Williams added 16 points and Kenneth Ortiz 10 for Wagner.
Monmouth bettered the Seahawks on the boards (34-33) and in turnover margin (11 for Monmouth and 12 for Wagner), but struggled at the free-throw line. The Hawks made just 58.3 percent from the line (14 of 24), while Wagner was 29 of 38 (76.3 percent).
Giving away one more turnover than the Hawks, Wagner snapped an 11-game streak of winning the turnover battle.
Jesse Steele led the Hawks (3-12, 1-3) with 20 points. Mike Myers Keitt added 16 points for Monmouth, which lost for the fifth time in its last six games.